Transcript Tools for APP in mathematics

Cippenham Infant School
Maths Workshop
Number and Calculations
6th February 2013
Believe and Achieve Together
We all use Maths all day everyday!
• We look at the clock to tell the time before we get out of
bed.
• We estimate how far it is to the floor!
• We know how many degrees to turn the tap so that we get
enough water without getting soaked!
• We measure the cornflakes in our bowl so they don't spill
over!
• We go to the shops, pay bills, pay for the bus…you get the
picture!
• Today we will focus on number and calculating and aim to
show you how we develop your child’s mathematical
knowledge at school and provide some ideas how you can
best support them at home.
Foundation Stage - How its Done!
Development Matters
• A document called Development Matters is used to plan
relevant activities and learning opportunities at age related
expectations.
• All activities are working towards the final aim, the Early
Learning Goal.
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What are the Early Learning Goals?
FS - Number
Children count reliably with numbers from one to 20,
place them in order and say which number is one
more or one less than a given number.
Using quantities and objects, they add and subtract
two single-digit numbers and count on or back to
find the answer.
They solve problems, including doubling, halving and
sharing.
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Key Stage One - How its Done!
The National Curriculum
• Many support materials such as ‘The Primary Strategies’ have been
produced to help teachers plan effectively and with progression.
• All support materials work towards the final goal to achieve National
Curriculum expectations.
• At Cippenham Infant School we use the National Curriculum and School
Targets to plan effectively for every child.
• Nationally pupils are expected to achieve level 2b at the end of year two,
although at Cippenham Infant School we always aim higher!
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KS1 – Number
Level 1
Count up to 10 objects
Read, write numbers to 10
Order numbers to 10
Understand addition as finding the total of two or more sets of
objects
Understand subtraction as ‘taking away’ objects from a set and
finding how many are left
Add and subtract numbers or objects to 10
Begin to know some addition facts
Solve addition and subtraction problems involving up to 10
objects (practically)
Record work with objects, pictures, diagrams
Begin to use + and =
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KS1 – Number
Level 2
Count sets reliably (10’s, 2’s 5’s)
Know place value of 2 digit numbers
Recognise odd and even numbers Use the knowledge that
subtraction is the inverse of addition
Understand halving as a way of ‘undoing’ doubling and
vice versa Use mental recall of addition facts to 10
Use mental calculation strategies to solve number
problems including those involving money and measures
Choose appropriate operation when solving addition and
subtraction problems
Solve number problems involving money and measures
Record their work number sentences
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Addition and Subtraction
First, we begin with fun practical activities.
You have 2 sweets. I give you 1 more.
How many do you have altogether?
You have 4 pencils. I take one away.
How many pencils do you have left?
Addition and Subtraction
Then, we learn how to write it as a number sentence.
2
4
+
-
1
1
=
=
3
3
Addition and subtraction
Using a numberline
8+5=?
Put your finger on 8….jump on 5…
What number did you land on?
15-7=?
Put your finger on 15….jump back 7….
What number did you land on?
Addition and subtraction
Have a go!
8+7=
We always remind the children to count the
jumps not the numbers!
Addition
Mental methods
15+3=18
“Put 15 in your head, count on 3.
What number did you land on?”
19-6=13
“Put 19 in your head, count back 6.
What number did you land on?”
The teachers like to call it ‘Grab and Chin It!’
Addition
Have a go!
18+6=?
‘Grab and Chin It!’
Addition and Subtraction
Using a hundred square
Once there is understanding of the value of Tens and Units we use the
100 Square to work out the answer.
15+12=?
“Put you finger on 15. Add 10 by
jumping down one row, then add 2 by
jumping along 2. What number did
you land on?”
27-14=?
“Put your finger on 27. Take away 10
by jumping up one row, then take
away 4 by jumping back 4. What
number did you land on?
Addition and subtraction
Mental methods and number sentences
Once there is understanding of the value of Tens and Units then we use
this method but remember we always keep the first number whole!
15+12=
37-26
15+10=25
37-20=17
25+2=27
17+6=11
The children use Dennes blocks to support their understanding. Also,
until they are confident at counting on and back in Tens and Units in
their head they can use a 100 square to check their answers.
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1
Addition and subtraction
Have a go at the long written method!
17+14=?
35-22=?
Remember we always keep
the first number whole!
Explain Multiplication
First, we begin with fun practical activities.
I have 5 friends coming to a party and each friend needs
2 slices of pizza for dinner. How many slices do I need?
Multiplication
Then, we learn how to write it as a number sentence.
First of all we teach the children to understand
‘x’ as ‘lots of’
So
So: 5 lots of 2 = 10
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Multiplication
Then, record with the multiplication operation symbol.
So:
5 x 2 = 10
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Multiplication
Repeated addition
When the children are still developing
their number skills, it can be useful to
show them how to work out
multiplication as repeated addition.
So 4 lots of 5 or 4 x 5
would become 5 + 5 + 5 + 5
And the answer is 20!
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Multiplication
I can multiply using arrays.
Multiplication
I can multiply using arrays.
I have 12 counters.
How could you arrange them
into 2 equal rows?
There are 2 lots of 6….
There are 2 lots of 6….
…..6 + 6 = 12
Or there are 6 lots of 2….
…. 2 + 2 + 2 + 2 + 2 + 2 = 12
Then you can convert these repeated
additions into multiplication number
sentences using ‘lots of’.
6 + 6 = 12
How many ‘lots of’ 6 are there?
So this becomes
2 lots of 6 = 12
or 2 x 6 = 12
Then you can convert these repeated
additions into multiplication number
sentences using ‘lots of’.
2 + 2 + 2 + 2 + 2 + 2 = 12
How many ‘lots of’ 2 are there?
So this becomes
6 lots of 2 = 12
or 6 x 2 = 12
Can you think of any other ways
to arrange the counters?
Write your repeated addition
and corresponding multiplication
on your board!
Multiplication
Mental methods
As the children progress in their learning of
mathematics, they will develop mental
strategies that will allow them to solve
multiplication problems without written
methods.
So calculating 5 x 2
involves counting in 2’s 5 times!
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Division
First, we begin with fun practical activities.
I have 8 cookies and need to share them with my friend.
How many cookies do we get each?
Division
We share the cookies between the 2 people.
How many cookies do they get each?
4
Division
Then we teach the children to write this as a number
sentence.
First of all we explain the division operation symbol as
meaning shared between.
So 8 shared between 2 = 4
Division
Then, record with the multiplication operation symbol.
So:
8÷2=4
Division
Mental methods
As the children progress in their learning of
mathematics, they will develop mental
strategies that will allow them to solve division
problems without written methods.
They can actually use their knowledge of
multiplication to help them with this.
Start on 4 and count in 4’s until you get to 8.
Count on your fingers how many times you
count. That’s your answer!
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Division
Repeated Subtraction
When the children are still developing
their number skills, it can be useful to
show them how to work out division as
repeated subtraction.
So you start on 8 and jump back in 2’s
until you can’t go any further!
How many jumps do you make?
2!
So 8 ÷ 2 = 4
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Using and Applying
During all maths activities the children need to be able to use and apply
what they know.
We have to ask the right questions to support the children in learning
how to use and apply their knowledge.
This is really important when solving real life problems.
I spend 35p at the shops. If I
pay with 50p how much change
will I get?
Using and Applying
?
What are the
important numbers?
What can you do
check your answer
is right?
What do you need to
do to work out the
answer?
What are the
important words?
How do you know?
Have a go!
Using any of the methods we have looked at today, what would be
the best method for the children to use to work out the answer?
Using and Applying
Level 1
Use mathematics as an integral part of classroom activities, (with support)
- engage with practical mathematical activities involving sorting, counting and measuring
by direct comparison
- begin to understand the relevance of mathematical ideas to everyday situations by
using them in role-play
Level 2
Select the mathematics they use in some classroom activities (with support)
- find a starting point, identifying key facts/relevant information
- use apparatus, diagrams, role-play, etc. to represent and clarify a problem
- move between different representations of a problem, e.g. a situation described in
words, a diagram, etc.
- adopt a suggested model or systematic approach
- make connections and apply their knowledge to similar situations
- use mathematical content from levels 1 and 2 to solve problems and investigate
Questions
Learning is a journey!
At CIS learning is exciting, challenging and personal.
Children should rarely stop on their school journey. If
and when they do we all need to be there to ensure they
continue rapidly and confidently to enable them to be
the best they can be.
How can you support your child on their learning
journey?
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How can you support your child on their learning
journey?
• Use school methods when completing homework.
• Share mathematical experiences that are fun – look at your
hand out for help!
• Day to day tasks are a mathematical opportunity!
Count the stairs to bed, look at even and odd numbers on houses,
add together the numbers on a car number plate, cutting a cake into
even slices…
• Play relevant learning games on the computer.
• One of the most valuable things you can do is to ask the
magic question...”How did you work it out?” If children can
explain what they have done they will consolidate their
own understanding and misconceptions can be addressed.
• Always ask the teachers if you have any questions.
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Families into maths
Tuesday 12th and Thursday 14th February
9.15am - 10.15am
We look forward to welcoming you into school.